Finite Group Databasebeta

← C2×#20254061 #27086151

Subgroups — C2×#20254061 #27086151

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689747C211yesmaximal, characteristic
2C2×#15689736C211yesmaximal, characteristic, complemented
3#20254061C2116yesmaximal, direct product factor
4C2×#15689517C211yesmaximal, characteristic, complemented
5C2×#15689480C211yesmaximal, characteristic, complemented
6C2×#15689475C211yesmaximal, characteristic, complemented
7C2×#15689382C211yesmaximal, characteristic, complemented
8C2×#15689370C211yesmaximal, characteristic
9C2×#15689365C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic
11C2×#15689229C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689217C211yesmaximal, characteristic, complemented
14C2×#15689210C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#501C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689747—24no—
24#15689747C2218yes—
25#15689736—24no—
26#15689736C2218yescomplemented
27C2×#13094024C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094019—21no—
30C2×#13094019—21no—
31C2×#13094015—21no—
32C2×#13094015—21no—
33C2×#13094013—21no—
34C2×#13094012C2211yescharacteristic
35C2×#13094009—21no—
36C2×#13094004C2211yescharacteristic
37C2×#13094004C2211yescharacteristic
38C2×#13094004C2211yescharacteristic
39C2×#13094000—21no—
40C2×#13093999C2211yescharacteristic
41C2×#13093989C2211yescharacteristic
42C2×#13093989C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46#15689517C2218yescomplemented
47#15689480C2218yescomplemented
48#15689475C2218yescomplemented
49#15689382C2218yescomplemented
50#15689370C2218yes—
51#15689365C2218yescomplemented
52#15689353C2218yes—
53#15689229C2218yescomplemented
54#15689222C2218yescomplemented
55#15689217C2218yescomplemented
56#15689210C2218yescomplemented
57C2×#13093947C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#15689080C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×C4×C47⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic
71C47×#501C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C22×C4×D47C2311yescharacteristic
84C2×Dic188—24no—
85C2×Dic188—24no—
86C2×Dic188C2314yes—
87C2×Dic188C2314yes—
88C2×#10625325—24no—
89C2×#10625325—24no—
90C2×#10625325C2314yes—
91C2×#10625325C2314yes—
92C2×#10625324—24no—
93C2×#10625324C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96C2×C8×D47—24no—
97C2×C8×D47C2314yes—
98#13094024—22no—
99#13094024C2314yes—
100#13094019—28no—
101#13094019—28no—
102#13094019—28no—
103#13094015—28no—
104#13094015—28no—
105#13094013—28no—
106#13094012—22no—
107#13094012C2314yes—
108#13094009—28no—
109#13094004—22no—
110#13094004—22no—
111#13094004—22no—
112#13094004C2314yes—
113#13094004C2314yes—
114#13094004C2314yes—
115#13094000—28no—
116#13093999—22no—
117#13093999C2314yes—
118#13093989—22no—
119#13093989—22no—
120#13093989—22no—
121#13093989C2314yes—
122#13093989C2314yes—
123#13093989C2314yes—
124#13093986—22no—
125#13093986C2314yes—
126#13093981D414yes—
127#13093981C2314yes—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C2×Dic47⋊C4D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×C4×Dic47—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47C2311yescharacteristic
151#13093947C2314yes—
152#13093947C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159#13093934C2314yes—
160C4×C47⋊C8C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—21no—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4⋊Q8×C47—22no—
166C4⋊Q8×C47C2314yes—
167#125×C47—22no—
168#125×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#107×C47C2314yes—
179#106×C47C2314yes—
180#106×C47C2314yes—
181#97×C47C2314yes—
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—24no—
185C2×Q8×C47—82no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2411yescharacteristic
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47C2×D411yescharacteristic
197C22×Dic47C2×D411yescharacteristic
198C22×Dic47C2×D411yescharacteristic
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—21no—
202C2×D188—24no—
203C2×D188—82no—
204C2×D188C2412yes—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—24no—
208C2×C4×D47—82no—
209C2×C4×D47C2×D412yes—
210C2×C4×D47C2412yes—
211C2×Dic94—22no—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—21no—
218C2×Dic94—21no—
219C2×Dic94—21no—
220C2×Dic94C2412yes—
221C2×Dic94C2412yes—
222C2×Dic94C2412yes—
223C2×C8×C47#4114yes—
224C2×C8×C47#4114yes—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4C2×D414yes—
248(C2×D47)⋊C4C2×D414yes—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4C2×D414yes—
258Dic47⋊C4C2×D414yes—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47C2×D412yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268Dic188—28no—
269Dic188—28no—
270#10625325—28no—
271#10625325—28no—
272#10625324—28no—
273C8×D47—28no—
274C23×C47C22×D411yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47C22×D412yes—
283Q8×C47—84no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4112yes—
298C2×C4×C47C2×#4112yes—
299C2×C4×C47C2511yescharacteristic
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C2×Dic47C22×D412yes—
312D188—22no—
313D188—22no—
314D188—42no—
315D188—84no—
316C4×D47—24no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—84no—
320Dic94—22no—
321Dic94—22no—
322Dic94—22no—
323Dic94—22no—
324Dic94—22no—
325Dic94—22no—
326Dic94—42no—
327Dic94—42no—
328Dic94—42no—
329C8×C47C2×#4114yes—
330C8×C47C2×#4114yes—
331C47⋊C8—22no—
332C47⋊C8—22no—
333C2×#3178—471nomaximal, Sylow
334C22×C47#53212yes—
335C22×C47#57712yes—
336C22×C47#57812yes—
337C22×C47C23×D411yescharacteristic
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—44no—
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—84no—
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47#53212yes—
353C4×C47C22×#4111yescharacteristic
354C4×C47C22×#4111yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#542—471no—
362C2×#541—471no—
363#3178—4716no—
364C2×#501D4711yescharacteristic, complemented
365C2×#497—471no—
366C2×#488—471no—
367C2×#487—471no—
368C2×#470—471no—
369C2×#468—471no—
370C2×#467—471no—
371C2×#465—471no—
372C2×#441—471no—
373C2×#440—471no—
374C2×C4×Q16—471no—
375C2×C4×SD16—471no—
376C2×#405—471no—
377C2×C47#317814yescomplemented
378C2×C47C2×#53211yescharacteristic
379C2×C47C2×#57711yescharacteristic
380C2×C47C2×#57811yescharacteristic
381D47—42no—
382D47—82no—
383C22×Q16—471no—
384C22×Q16—471no—
385C22×SD16—471no—
386C22×SD16—471no—
387C22×M16—471no—
388C23×C8—471no—
389#542—478no—
390#542—944no—
391#541—478no—
392#541—944no—
393C2×C4⋊Q8—471no—
394C2×C4⋊Q8C2×D4711yescharacteristic
395C2×#126—941no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#125—941no—
399C2×#125—941no—
400C2×#125C2×D4711yescharacteristic
401C2×#124—471no—
402C2×#124—941no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—471no—
407C2×C22⋊Q8—941no—
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×D4—471no—
413C2×#117—471no—
414#501C2×D4718yescomplemented
415#497—478no—
416#488—478no—
417#487—478no—
418#470—478no—
419#468—478no—
420#467—478no—
421#465—478no—
422#441—478no—
423#440—478no—
424C4×Q16—478no—
425C4×SD16—478no—
426C2×#107C2×D4711yescharacteristic
427C2×#107C2×D4711yescharacteristic
428C2×#106C2×D4711yescharacteristic
429C2×#106C2×D4711yescharacteristic
430C2×#103—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#102—471no—
437C2×#102—471no—
438#405—478no—
439C2×#97—471no—
440C2×#97C2×D4711yescharacteristic
441C2×C4×C8—471no—
442C2×C4×C8—471no—
443C47C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—21no—
445C22×Q8—471no—
446C22×Q8—471no—
447C22×Q8—471no—
448C22×D4—471no—
449C22×D4—941no—
450C23×C4—471no—
451C23×C4—941no—
452C2×Q16—474no—
453C2×Q16—474no—
454C2×Q16—944no—
455C2×Q16—944no—
456C2×SD16—474no—
457C2×SD16—474no—
458C2×SD16—944no—
459C2×SD16—944no—
460C2×M16—474no—
461C2×M16—944no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—474no—
465C22×C8—944no—
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—474no—
470C4⋊Q8—942no—
471C4⋊Q8C22×D4714yes—
472#126—948no—
473#126—948no—
474#126—948no—
475#125—22no—
476#125—948no—
477#125—948no—
478#125C22×D4714yes—
479#124—474no—
480#124—948no—
481#124—942no—
482#123—948no—
483C22⋊Q8—474no—
484C22⋊Q8—474no—
485C22⋊Q8—474no—
486C22⋊Q8—942no—
487C22⋊Q8—942no—
488C22⋊Q8—942no—
489C22⋊Q8—948no—
490#121—474no—
491#121—942no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×D4—474no—
499C4×D4—942no—
500#117—474no—
501#117—474no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4C22×D4711yescharacteristic
516C2×C4⋊C4C22×D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—471no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42—941no—
532C2×C42C22×D4711yescharacteristic
533#107C22×D4714yes—
534#107C22×D4714yes—
535#106C22×D4714yes—
536#106C22×D4714yes—
537#103—474no—
538#103—474no—
539#103—474no—
540#103—474no—
541#103—474no—
542#103—474no—
543#102—474no—
544#102—474no—
545#97—474no—
546#97C22×D4714yes—
547C4×C8—474no—
548C4×C8—474no—
549C24—471no—
550C24—941no—
551C2×Q8—24no—
552C2×Q8—82no—
553C2×Q8—472no—
554C2×Q8—472no—
555C2×Q8—472no—
556C2×Q8—941no—
557C2×Q8—941no—
558C2×Q8—941no—
559C2×Q8—942no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—942no—
564C2×Q8—942no—
565C2×D4—472no—
566C2×D4—944no—
567C2×D4—941no—
568C2×D4—942no—
569C2×D4—942no—
570C2×D4—3762no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—471no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—944no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—3762no—
587C22×C4D4×D4711yescharacteristic
588C22×C4D4×D4711yescharacteristic
589C22×C4C23×D4711yescharacteristic
590Q16—948no—
591Q16—948no—
592SD16—948no—
593SD16—948no—
594M16—948no—
595C2×C8—472no—
596C2×C8—472no—
597C2×C8—942no—
598C2×C8—942no—
599C2×C8—948no—
600C2×C8#1062535414yes—
601C2×C8#1062535414yes—
602C2×C8C23×D4712yes—
603C2×C8C23×D4712yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—474no—
612C4⋊C4—474no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C4⋊C4C23×D4712yes—
624C4⋊C4C23×D4712yes—
625C22⋊C4—474no—
626C22⋊C4—474no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C42—472no—
635C42—472no—
636C42—944no—
637C42—944no—
638C42—944no—
639C42D4×D4712yes—
640C42C23×D4712yes—
641C23—472no—
642C23—942no—
643C23—942no—
644C23—942no—
645C23—942no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23C2×D4×D4711yescharacteristic
650Q8—84no—
651Q8—942no—
652Q8—942no—
653Q8—942no—
654Q8—942no—
655Q8—942no—
656Q8—942no—
657Q8—1882no—
658Q8—1882no—
659Q8—1882no—
660D4—942no—
661D4—942no—
662D4—3764no—
663D4—1882no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—944no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—3764no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4C2×D4×D4712yes—
691C2×C4C2×D4×D4712yes—
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4C2×#1062535412yes—
694C2×C4C2×#1062535412yes—
695C2×C4C24×D4711yescharacteristic
696C8—942no—
697C8—942no—
698C8C2×#1062535414yes—
699C8C2×#1062535414yes—
700C22—942no—
701C22—942no—
702C22—942no—
703C22—3764no—
704C22—1882no—
705C22—1882no—
706C22—1882no—
707C22—1884no—
708C22#1568967412yes—
709C22#1568993312yes—
710C22#1568993912yes—
711C22C22×D4×D4711yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4#1568967412yes—
725C4C22×#1062535411yescharacteristic
726C4C22×#1062535411yescharacteristic
727C2—3762no—
728C2—1882no—
729C2#2025406114yesdirect product factor
730C2C2×#1568967411yescharacteristic
731C2C2×#1568993311yescharacteristic
732C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
prime radicalC2×#13093999C22
hypercenterC2×#501D47
hypocenterC47C2×#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#15689736C2semidirect
3. #20254061C2direct (N × H)
4. C2×#15689517C2semidirect
5. C2×#15689480C2semidirect
6. C2×#15689475C2semidirect
7. C2×#15689382C2semidirect
9. C2×#15689365C2semidirect
11. C2×#15689229C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689217C2semidirect
14. C2×#15689210C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#501C2semidirect
26. #15689736C22semidirect
46. #15689517C22semidirect
47. #15689480C22semidirect
48. #15689475C22semidirect
49. #15689382C22semidirect
51. #15689365C22semidirect
53. #15689229C22semidirect
54. #15689222C22semidirect
55. #15689217C22semidirect
56. #15689210C22semidirect
65. #15689080C22semidirect
71. C47×#501C22semidirect
364. C2×#501D47semidirect
377. C2×C47#3178semidirect
414. #501C2×D47semidirect
443. C47C2×#3178semidirect
729. C2#20254061direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156897472
C2×#156897362
#202540612
C2×#156895172
C2×#156894802
C2×#156894752
C2×#156893822
C2×#156893702
C2×#156893652
C2×#156893532
C2×#156892292
C2×#156892222
C2×#156892172
C2×#156892102
C2×#156890802
C2×C47×#5012
C2×#317847